Robert, 54, who held Swiss nationality, had been operated on in Iraq and then flown back for treatment in France overnight Thursday to Friday, but died of her wounds, the public broadcaster said in a statement.
French colleague Stephan Villeneuve and Iraqi Kurdish reporter Bakhtiyar Addad were also killed in Monday's blast.
All three were working for production company #5 Bis Productions on a programme for the French news programme Envoye Special, aired on public television channel France 2.
A fourth journalist with them, Samuel Forey, suffered light injuries.
French Culture Minister Francoise Nyssen paid tribute to a “great war correspondent”, in a post on the ministerial Twitter account.
Robert was an experienced war correspondent specialising in coverage of the Middle East, Iraq in particular, said the statement from France Televisions.
She worked for several news outlets in France and Switzerland, including Le Figaro newspaper and Paris Match magazine. Robert has two adult sons.
The journalists were accompanying Iraqi special forces during the battle for Mosul, where jihadists from the Islamic State group entrenched in the narrow streets of the Old City have set numerous booby traps.
France Televisions and #5 Bis Productions paid tribute to Robert's work and offered their condolences to her family in the statement.
Emilie Raffoul, a producer at #5 Bis Productions, told AFP: “She was someone who was very determined.”
On Tuesday, the day after the landmine blast, Raffoul flew to Iraq to take care of Robert, along with colleagues from France Televisions.
The US doctors who had treated her at a military hospital said that even in a coma, Robert seemed mentally very strong, she added.
“She was used to combat zones, she was a professional war (correspondent)
who had covered several conflicts, a specialist in the Middle East,” said Raffoul, who worked with Robert for around 15 years.
“She was extremely rigorous in the preparation of her reports,” she added.
Robert's producer Nicolas Jaillard wrote in a Facebook post that they had been hoping for better news. “The word sadness is not enough to describe how we feel,” he added.
Reporters without Borders (RSF), the Paris-based media rights watchdog, also saluted her.
In comments on his Twitter account RSF secretary-general Christophe Deloire lamented the fact that too many foreign correspondents were being killed on the front line.
According to RSF's own tally, her death brings to 29 the number of journalists killed in Iraq since 2014.
On Tuesday, the French president's office announced that Villeneuve would be posthumously awarded the knight of the Legion of Honour, one of France's highest honours.